The voting is open to all registered residents, Kurds and non-Kurds, in the Kurdish-held areas in northern Iraq aged 18 or over.
France is a main partner in the US-led coalition helping Baghdad fight the militants who seized parts of Iraq and Syria in 2014.
Iraq’s Yazidis marked three years since Islamic State launched what the UN said was a genocidal campaign against them on Thursday, but their ordeal is far from over despite the ouster of the jihadist fighters.
While there is no clear successor at the moment, the top two contenders are Iyad al-Obaidi and Ayad al-Jumaili, Baghdadi’s top lieutenants.
The decision is likely to get a lot of opposition by the government which earlier this year had made an unsuccessful resolution to lower Kurdish flags flown in the region.
Up to 200,000 people still live behind ISIS lines in Mosul’s Old City and three other districts.
Influential cleric Moqtada al-Sadr and Iran backed Nuri-al-Maliki are locked in a tussle to gain enough power before the upcoming elections.
ISIS claimed a series of suicide attacks that killed at least 14 people south and west of Baghdad on Monday.
ISIS’s assault on Kirkuk, which lies in an oil-producing region, killed six members of the security forces and two Iranians
The battle in Falluja has allowed Abadi to shift the focus domestically away from a crisis that unfolded when he failed to push through a cabinet reshuffle he sought as part of his drive to fight corruption.
The assault on Falluja has begun what is expected to be one of the biggest battles ever fought against Islamic State. About 50,000 civilians remain in the city, according to the United Nations.